Suppose that $x$ is a positive multiple of $3$. If $x$ cubed is less than $1000$, what is the greatest possible value of $x$?
Answer: Ten cubed is 1000, so we know that $x$ must be less than $10$. Because $9$ is the greatest multiple of $3$ that is less than $10$, $\boxed{9}$ is the greatest possible value of $x$.